/*
* RELIC is an Efficient LIbrary for Cryptography
* Copyright (c) 2009 RELIC Authors
*
* This file is part of RELIC. RELIC is legal property of its developers,
* whose names are not listed here. Please refer to the COPYRIGHT file
* for contact information.
*
* RELIC is free software; you can redistribute it and/or modify it under the
* terms of the version 2.1 (or later) of the GNU Lesser General Public License
* as published by the Free Software Foundation; or version 2.0 of the Apache
* License as published by the Apache Software Foundation. See the LICENSE files
* for more details.
*
* RELIC is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the LICENSE files for more details.
*
* You should have received a copy of the GNU Lesser General Public or the
* Apache License along with RELIC. If not, see
* or .
*/
/**
* @defgroup pp Bilinear pairings over prime elliptic curves.
*/
/**
* @file
*
* Interface of the module for computing bilinear pairings over prime elliptic
* curves.
*
* @ingroup pp
*/
#ifndef RLC_PP_H
#define RLC_PP_H
#include "relic_fpx.h"
#include "relic_epx.h"
#include "relic_types.h"
/*============================================================================*/
/* Macro definitions */
/*============================================================================*/
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 2.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] P - the second point to add.
* @param[in] Q - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_add_k2(L, R, P, Q) pp_add_k2_basic(L, R, P, Q)
#else
#define pp_add_k2(L, R, P, Q) pp_add_k2_projc(L, R, P, Q)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 2 using projective
* coordinates.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] P - the second point to add.
* @param[in] Q - the affine point to evaluate the line function.
*/
#if PP_EXT == BASIC
#define pp_add_k2_projc(L, R, P, Q) pp_add_k2_projc_basic(L, R, P, Q)
#else
#define pp_add_k2_projc(L, R, P, Q) pp_add_k2_projc_lazyr(L, R, P, Q)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] Q - the second point to add.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_add_k8(L, R, Q, P) pp_add_k8_basic(L, R, Q, P)
#else
#define pp_add_k8(L, R, Q, P) pp_add_k8_projc(L, R, Q, P)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using projective
* coordinates.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] Q - the second point to add.
* @param[in] P - the affine point to evaluate the line function.
*/
#if PP_EXT == BASIC
#define pp_add_k8_projc(L, R, Q, P) pp_add_k8_projc_basic(L, R, Q, P)
#elif PP_EXT == LAZYR
#define pp_add_k8_projc(L, R, Q, P) pp_add_k8_projc_lazyr(L, R, Q, P)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] Q - the second point to add.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_add_k12(L, R, Q, P) pp_add_k12_basic(L, R, Q, P)
#else
#define pp_add_k12(L, R, Q, P) pp_add_k12_projc(L, R, Q, P)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] Q - the second point to add.
* @param[in] P - the affine point to evaluate the line function.
*/
#if PP_EXT == BASIC
#define pp_add_k12_projc(L, R, Q, P) pp_add_k12_projc_basic(L, R, Q, P)
#elif PP_EXT == LAZYR
#define pp_add_k12_projc(L, R, Q, P) pp_add_k12_projc_lazyr(L, R, Q, P)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 48.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] Q - the second point to add.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_add_k48(L, RX, RY, RZ, QX, QY, P) pp_add_k48_basic(L, RX, RY, QX, QY, P)
#else
#define pp_add_k48(L, RX, RY, RZ, QX, QY, P) pp_add_k48_projc(L, RX, RY, RZ, QX, QY, P)
#endif
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 54.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point and first point to add.
* @param[in] Q - the second point to add.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_add_k54(L, RX, RY, RZ, QX, QY, P) pp_add_k54_basic(L, RX, RY, QX, QY, P)
#else
#define pp_add_k54(L, RX, RY, RZ, QX, QY, P) pp_add_k54_projc(L, RX, RY, RZ, QX, QY, P)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 2.
*
* @param[out] L - the result of the evaluation.
* @param[out] R - the resulting point.
* @param[in] P - the point to double.
* @param[in] Q - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_dbl_k2(L, R, P, Q) pp_dbl_k2_basic(L, R, P, Q)
#else
#define pp_dbl_k2(L, R, P, Q) pp_dbl_k2_projc(L, R, P, Q)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8.
*
* @param[out] L - the result of the evaluation.
* @param[out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_dbl_k8(L, R, Q, P) pp_dbl_k8_basic(L, R, Q, P)
#else
#define pp_dbl_k8(L, R, Q, P) pp_dbl_k8_projc(L, R, Q, P)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12.
*
* @param[out] L - the result of the evaluation.
* @param[out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_dbl_k12(L, R, Q, P) pp_dbl_k12_basic(L, R, Q, P)
#else
#define pp_dbl_k12(L, R, Q, P) pp_dbl_k12_projc(L, R, Q, P)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if PP_EXT == BASIC
#define pp_dbl_k8_projc(L, R, Q, P) pp_dbl_k8_projc_basic(L, R, Q, P)
#elif PP_EXT == LAZYR
#define pp_dbl_k8_projc(L, R, Q, P) pp_dbl_k8_projc_lazyr(L, R, Q, P)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 2 using projective
* coordinates.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if PP_EXT == BASIC
#define pp_dbl_k2_projc(L, R, P, Q) pp_dbl_k2_projc_basic(L, R, P, Q)
#elif PP_EXT == LAZYR
#define pp_dbl_k2_projc(L, R, P, Q) pp_dbl_k2_projc_lazyr(L, R, P, Q)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] L - the result of the evaluation.
* @param[in, out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if PP_EXT == BASIC
#define pp_dbl_k12_projc(L, R, Q, P) pp_dbl_k12_projc_basic(L, R, Q, P)
#elif PP_EXT == LAZYR
#define pp_dbl_k12_projc(L, R, Q, P) pp_dbl_k12_projc_lazyr(L, R, Q, P)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 48.
*
* @param[out] L - the result of the evaluation.
* @param[out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_dbl_k48(L, RX, RY, RZ, P) pp_dbl_k48_basic(L, RX, RY, P)
#else
#define pp_dbl_k48(L, RX, RY, RZ, P) pp_dbl_k48_projc(L, RX, RY, RZ, P)
#endif
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 54.
*
* @param[out] L - the result of the evaluation.
* @param[out] R - the resulting point.
* @param[in] Q - the point to double.
* @param[in] P - the affine point to evaluate the line function.
*/
#if EP_ADD == BASIC
#define pp_dbl_k54(L, RX, RY, RZ, P) pp_dbl_k54_basic(L, RX, RY, P)
#else
#define pp_dbl_k54(L, RX, RY, RZ, P) pp_dbl_k54_projc(L, RX, RY, RZ, P)
#endif
/**
* Computes a pairing of two prime elliptic curve points defined on an elliptic
* curves of embedding degree 2. Computes e(P, Q).
*
* @param[out] R - the result.
* @param[in] P - the first elliptic curve point.
* @param[in] Q - the second elliptic curve point.
*/
#if PP_MAP == TATEP
#define pp_map_k2(R, P, Q) pp_map_tatep_k2(R, P, Q)
#elif PP_MAP == WEILP
#define pp_map_k2(R, P, Q) pp_map_weilp_k2(R, P, Q)
#elif PP_MAP == OATEP
#define pp_map_k2(R, P, Q) pp_map_tatep_k2(R, P, Q)
#endif
/**
* Computes a pairing of two prime elliptic curve points defined on an elliptic
* curve of embedding degree 12. Computes e(P, Q).
*
* @param[out] R - the result.
* @param[in] P - the first elliptic curve point.
* @param[in] Q - the second elliptic curve point.
*/
#if PP_MAP == TATEP
#define pp_map_k12(R, P, Q) pp_map_tatep_k12(R, P, Q)
#elif PP_MAP == WEILP
#define pp_map_k12(R, P, Q) pp_map_weilp_k12(R, P, Q)
#elif PP_MAP == OATEP
#define pp_map_k12(R, P, Q) pp_map_oatep_k12(R, P, Q)
#endif
/**
* Computes a multi-pairing of elliptic curve points defined on an elliptic
* curve of embedding degree 2. Computes \prod e(P_i, Q_i).
*
* @param[out] R - the result.
* @param[in] P - the first pairing arguments.
* @param[in] Q - the second pairing arguments.
* @param[in] M - the number of pairings to evaluate.
*/
#if PP_MAP == WEILP
#define pp_map_sim_k2(R, P, Q, M) pp_map_sim_weilp_k2(R, P, Q, M)
#elif PP_MAP == TATEP || PP_MAP == OATEP
#define pp_map_sim_k2(R, P, Q, M) pp_map_sim_tatep_k2(R, P, Q, M)
#endif
/**
* Computes a multi-pairing of elliptic curve points defined on an elliptic
* curve of embedding degree 12. Computes \prod e(P_i, Q_i).
*
* @param[out] R - the result.
* @param[in] P - the first pairing arguments.
* @param[in] Q - the second pairing arguments.
* @param[in] M - the number of pairings to evaluate.
*/
#if PP_MAP == TATEP
#define pp_map_sim_k12(R, P, Q, M) pp_map_sim_tatep_k12(R, P, Q, M)
#elif PP_MAP == WEILP
#define pp_map_sim_k12(R, P, Q, M) pp_map_sim_weilp_k12(R, P, Q, M)
#elif PP_MAP == OATEP
#define pp_map_sim_k12(R, P, Q, M) pp_map_sim_oatep_k12(R, P, Q, M)
#endif
/*============================================================================*/
/* Function prototypes */
/*============================================================================*/
/**
* Initializes the pairing over prime fields.
*/
void pp_map_init(void);
/**
* Finalizes the pairing over prime fields.
*/
void pp_map_clean(void);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 2 using affine coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] p - the second point to add.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_add_k2_basic(fp2_t l, ep_t r, ep_t p, ep_t q);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] p - the second point to add.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_add_k2_projc_basic(fp2_t l, ep_t r, ep_t p, ep_t q);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates and lazy reduction.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] p - the second point to add.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_add_k2_projc_lazyr(fp2_t l, ep_t r, ep_t p, ep_t q);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using affine coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k8_basic(fp8_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k8_projc_basic(fp8_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using projective
* coordinates and lazy reduction.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k8_projc_lazyr(fp8_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using affine coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k12_basic(fp12_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k12_projc_basic(fp12_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates and lazy reduction.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k12_projc_lazyr(fp12_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve twist with embedding degree 12 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] p - the second point to add.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_add_lit_k12(fp12_t l, ep_t r, ep_t p, ep2_t q);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 48 using affine coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k48_basic(fp48_t l, fp8_t rx, fp8_t ry, fp8_t qx, fp8_t qy, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 48 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k48_projc(fp48_t l, fp8_t rx, fp8_t ry, fp8_t rz, fp8_t qx, fp8_t qy, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 54 using affine coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k54_basic(fp54_t l, fp9_t rx, fp9_t ry, fp9_t qx, fp9_t qy, ep_t p);
/**
* Adds two points and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 54 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point and first point to add.
* @param[in] q - the second point to add.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_add_k54_projc(fp54_t l, fp9_t rx, fp9_t ry, fp9_t rz, fp9_t qx, fp9_t qy, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 2 using affine
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] p - the point to double.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_dbl_k2_basic(fp2_t l, ep_t r, ep_t p, ep_t q);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] p - the point to double.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_dbl_k2_projc_basic(fp2_t l, ep_t r, ep_t p, ep_t q);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates and lazy reduction.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] p - the point to double.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_dbl_k2_projc_lazyr(fp2_t l, ep_t r, ep_t p, ep_t q);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using affine
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k8_basic(fp8_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k8_projc_basic(fp8_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 8 using projective
* coordinates and lazy reduction.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k8_projc_lazyr(fp8_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using affine
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k12_basic(fp12_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k12_projc_basic(fp12_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 12 using projective
* coordinates and lazy reduction.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k12_projc_lazyr(fp12_t l, ep2_t r, ep2_t q, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 48 using affine
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k48_basic(fp48_t l, fp8_t rx, fp8_t ry, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 48 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k48_projc(fp48_t l, fp8_t rx, fp8_t ry, fp8_t rz, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 54 using affine
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k54_basic(fp54_t l, fp9_t rx, fp9_t ry, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve with embedding degree 54 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] q - the point to double.
* @param[in] p - the affine point to evaluate the line function.
*/
void pp_dbl_k54_projc(fp54_t l, fp9_t rx, fp9_t ry, fp9_t rz, ep_t p);
/**
* Doubles a point and evaluates the corresponding line function at another
* point on an elliptic curve twist with embedding degree 12 using projective
* coordinates.
*
* @param[out] l - the result of the evaluation.
* @param[in, out] r - the resulting point.
* @param[in] p - the point to double.
* @param[in] q - the affine point to evaluate the line function.
*/
void pp_dbl_lit_k12(fp12_t l, ep_t r, ep_t p, ep2_t q);
/**
* Computes the final exponentiation for a pairing defined over curves of
* embedding degree 2. Computes c = a^(p^2 - 1)/r.
*
* @param[out] c - the result.
* @param[in] a - the extension field element to exponentiate.
*/
void pp_exp_k2(fp2_t c, fp2_t a);
/**
* Computes the final exponentiation for a pairing defined over curves of
* embedding degree 8. Computes c = a^(p^8 - 1)/r.
*
* @param[out] c - the result.
* @param[in] a - the extension field element to exponentiate.
*/
void pp_exp_k8(fp8_t c, fp8_t a);
/**
* Computes the final exponentiation for a pairing defined over curves of
* embedding degree 12. Computes c = a^(p^12 - 1)/r.
*
* @param[out] c - the result.
* @param[in] a - the extension field element to exponentiate.
*/
void pp_exp_k12(fp12_t c, fp12_t a);
/**
* Computes the final exponentiation for a pairing defined over curves of
* embedding degree 48. Computes c = a^(p^48 - 1)/r.
*
* @param[out] c - the result.
* @param[in] a - the extension field element to exponentiate.
*/
void pp_exp_k48(fp48_t c, fp48_t a);
/**
* Computes the final exponentiation for a pairing defined over curves of
* embedding degree 54. Computes c = a^(p^54 - 1)/r.
*
* @param[out] c - the result.
* @param[in] a - the extension field element to exponentiate.
*/
void pp_exp_k54(fp54_t c, fp54_t a);
/**
* Normalizes the accumulator point used inside pairing computation defined
* over curves of embedding degree 2.
*
* @param[out] r - the resulting point.
* @param[in] p - the point to normalize.
*/
void pp_norm_k2(ep_t c, ep_t a);
/**
* Normalizes the accumulator point used inside pairing computation defined
* over curves of embedding degree 8.
*
* @param[out] r - the resulting point.
* @param[in] p - the point to normalize.
*/
void pp_norm_k8(ep2_t c, ep2_t a);
/**
* Normalizes the accumulator point used inside pairing computation defined
* over curves of embedding degree 12.
*
* @param[out] r - the resulting point.
* @param[in] p - the point to normalize.
*/
void pp_norm_k12(ep2_t c, ep2_t a);
/**
* Computes the Tate pairing of two points in a parameterized elliptic curve
* with embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_tatep_k2(fp2_t r, ep_t p, ep_t q);
/**
* Computes the Tate multi-pairing of in a parameterized elliptic curve with
* embedding degree 2.
*
* @param[out] r - the result.
* @param[in] q - the first pairing arguments.
* @param[in] p - the second pairing arguments.
* @param[in] m - the number of pairings to evaluate.
*/
void pp_map_sim_tatep_k2(fp2_t r, ep_t *p, ep_t *q, int m);
/**
* Computes the Weil pairing of two points in a parameterized elliptic curve
* with embedding degree 2.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_weilp_k2(fp2_t r, ep_t p, ep_t q);
/**
* Computes the optimal ate pairing of two points in a parameterized elliptic
* curve with embedding degree 8.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_oatep_k8(fp8_t r, ep_t p, ep2_t q);
/**
* Computes the Weil multi-pairing of in a parameterized elliptic curve with
* embedding degree 2.
*
* @param[out] r - the result.
* @param[in] q - the first pairing arguments.
* @param[in] p - the second pairing arguments.
* @param[in] m - the number of pairings to evaluate.
*/
void pp_map_sim_weilp_k2(fp2_t r, ep_t *p, ep_t *q, int m);
/**
* Computes the Tate pairing of two points in a parameterized elliptic curve
* with embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_tatep_k12(fp12_t r, ep_t p, ep2_t q);
/**
* Computes the Tate multi-pairing of in a parameterized elliptic curve with
* embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first pairing arguments.
* @param[in] p - the second pairing arguments.
* @param[in] m - the number of pairings to evaluate.
*/
void pp_map_sim_tatep_k12(fp12_t r, ep_t *p, ep2_t *q, int m);
/**
* Computes the Weil pairing of two points in a parameterized elliptic curve
* with embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_weilp_k12(fp12_t r, ep_t p, ep2_t q);
/**
* Computes the Weil multi-pairing of in a parameterized elliptic curve with
* embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first pairing arguments.
* @param[in] p - the second pairing arguments.
* @param[in] m - the number of pairings to evaluate.
*/
void pp_map_sim_weilp_k12(fp12_t r, ep_t *p, ep2_t *q, int m);
/**
* Computes the optimal ate pairing of two points in a parameterized elliptic
* curve with embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_oatep_k12(fp12_t r, ep_t p, ep2_t q);
/**
* Computes the optimal ate multi-pairing of in a parameterized elliptic
* curve with embedding degree 12.
*
* @param[out] r - the result.
* @param[in] q - the first pairing arguments.
* @param[in] p - the second pairing arguments.
* @param[in] m - the number of pairings to evaluate.
*/
void pp_map_sim_oatep_k12(fp12_t r, ep_t *p, ep2_t *q, int m);
/**
* Computes the Optimal Ate pairing of two points in a parameterized elliptic
* curve with embedding degree 48.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_k48(fp48_t r, ep_t p, fp8_t qx, fp8_t qy);
/**
* Computes the Optimal Ate pairing of two points in a parameterized elliptic
* curve with embedding degree 54.
*
* @param[out] r - the result.
* @param[in] q - the first elliptic curve point.
* @param[in] p - the second elliptic curve point.
*/
void pp_map_k54(fp54_t r, ep_t p, fp9_t qx, fp9_t qy);
#endif /* !RLC_PP_H */